Lecture 2: Frictional unemployment

1. Lecture 2: Frictional unemployment I. The matching function

2. Frictional unemployment • We have seen foundations for «  classical unemployment » • Frictional unemployment arises from continuous reallocation of workers between jobs • In the models we have seen, unemployment would fall to zero absent the rigidities • We need to enrich these models

3. Questions we want to ask • What fraction of average unemployment is frictional? • Does frictional unemployment play a useful social role? • If so, what is the efficient level of unemployment? • How is frictional unemployment affected by growth, creative destruction, etc…? • Does the frictional component fluctuate?

4. The matching function • Costly process of allocation unemployed workers to vacant positions • The matching function is the production function for the flow of new hires • The inputs are: • The stock of unemployed workers looking for jobs • The stock of vacant jobs looking for workers

5. Hirings per unit of time • It is assumed to have the properties of a production function: • Constant returns to scale • Increasing in its arguments • Concave

6. The dynamics of unemployment

7. The Beveridge curve v du/dt = 0 u

8. Properties of the Beveridge Curbve • Steady state relationship between u and v • Downward sloping • Convex • The analysis can also be made in the (u,θ) plane where θ = v/u

9. The Beveridge curve θ du/dt = 0 u

10. Closing the model: labor demand

11. Closing the model: posting vacancies

12. The equilibrium value of θ

13. The equilibrium trajectory: θ du/dt = 0 u

14. Labor demand shocks • The θ falls when • c goes up • r goes up • φ goes up • y goes down • In steady state, this is associated with moves along the Beveridge curve

15. A fall in labor demand: θ E E’ u

16. In (u,v): v E E’ u

17. Reallocation shocks • We model it as an increase in s • The Beveridge curve shifts out (why?) • The labor demand curve shifts down • An increase in s is also a negative labor demand shock (why?)

18. An increase in s: θ E E’ u

19. In (u,v): v E E’ u

20. A deterioration in the matching process • The Beveridge curve shifts out again • No effect of labor demand • Contrary to a (pure) reallocation shock, labor flows fall

21. Business cycles • We can approximmate them by repeated switches between two values of y • They lead to loops around the Beveridge curve • Vacancies « lead » the cycle • Unemployment lags the cycle

22. The Loop: v u

23. Long-term unemployment • The model can be used to have heterogeneous search intensity among the unemployed • LTU: lower search intensity than STU • And fraction of LTU larger after recessions •  the Beveridge curve deteriorates • Persistent effects of transitory shocks

24. How do we do it?